Evaluating Functions

Lesson Overview

This 45-minute lesson is designed for Year 7-10 students, including those in support units with autism, behavioural, and mental health challenges, working at levels ranging approximately from Year 2 to Year 7. The lesson focuses on evaluating functions — substituting given inputs into algebraic expressions/functions to find outputs. The unit is "Algebra in Everyday Life," and this is lesson 16 of 30. The lesson strongly aligns with the NSW Mathematics Curriculum for Years 7-10, particularly outcomes related to the use of algebraic expressions and substitution.

NSW Curriculum Alignment

Stage: Year 7 – 10 (with differentiation for lower levels) Content Descriptions:

Use algebraic expressions to represent relationships between variables, substitute values into formulas, and solve for unknowns (Year 7)
Create tables of values related to algebraic expressions and describe the effect of variation (Year 7)
Use mathematical modelling to solve practical problems by substituting values into formulas (Years 8-10)

Achievement Standards (selected relevance):

Students use algebraic expressions to represent real-life situations, substitute values into formulas, and solve problems.
Students create tables and graphs from algebraic expressions, describing patterns and variations.
Students solve linear and related equations using appropriate methods.

These alignments correspond with outcomes described in the NSW syllabus documents for Years 7-10 mathematics.

Learning Objectives

By the end of this lesson, students will be able to:

Understand what a function represents as a rule relating an input to an output.
Correctly substitute given input values into a variety of functions (expressions with one or more variables).
Calculate and interpret the output values for given inputs.
Make connections between algebraic substitution and everyday contexts (authentic practical examples).
Demonstrate understanding through guided practice and independent problems.

Resources Needed

Whiteboard/interactive board
Pre-prepared worksheet with simple to moderate function evaluation problems and real-world contexts
Calculators (optional for advanced learners or those who need it)
Visual aids with step-by-step substitution examples (dyslexia-friendly formatting with clear fonts, spacing and colour-coded variables)
Digital tools (optional): simple function evaluators or graphing apps for demonstration

Lesson Breakdown

Time	Activity	Description	Differentiation / Notes
0-5 mins	Introduction & Recap	Briefly revisit what algebraic expressions and variables represent. Introduce “function” as a rule that assigns outputs to inputs. Use simple terms and visuals.	Use clear language; visuals and simple everyday examples (e.g., “If you get 2 apples per tree, how many apples do you get from 3 trees?”)
5-10 mins	Example 1 - Guided substitution	Demonstrate substitution with a simple linear function, eg. f(x) = 2x + 3. Write out input and output table. Use colour cues to highlight variables and numbers.	Use physical manipulatives or cards with numbers for hands-on substitution for students who benefit from tactile learning.
10-20 mins	Practice 1 - Structured worksheet	Students complete problems involving substitution into functions such as: f(x) = 3x - 1, g(x) = x² + 2, h(x, y) = 2x + y with provided inputs. Worksheets include real-life contexts like calculating total cost given price per item and quantity.	Scaffold task by providing step-by-step boxes, partially filled tables. Use coloured overlays/glass screens for reading ease for dyslexic students. Provide numeric input cards for manipulation if needed.
20-25 mins	Break/Brain break	Short movement/stretching break with visual countdown timer for predictability.	Sensory-friendly space for students who might need a quiet moment.
25-35 mins	Practice 2 - Real-life problem solving	Present authentic scenarios:

Calculating total pay given hours worked and hourly rate (using substitution into formula)
Determining perimeter/volume with variable side lengths Split class: Support students work on concrete substitution problems, advanced learners tackle functions with two variables or evaluate functions for multiple inputs and discuss patterns in outputs. | Support: One-on-one help or use of calculators. Advanced: Challenge with creating own input-output tables or simple graphing. | | 35-40 mins | Extension task | Advanced students write their own simple functions from word problems or describe the effect of changing inputs (e.g., doubling input doubles output) visually or verbally. | Opportunity for oral explanation for students who struggle with writing. | | 40-45 mins | Review & Assessment | Wrap-up as a whole class with a quick interactive quiz/game (e.g., mini whiteboards or Kahoot-style quiz) to assess understanding. Discuss any common misconceptions. | Encourage peer support. Provide immediate, positive feedback. |

Differentiation Strategies

Multi-sensory teaching: Incorporate visual, auditory, and tactile learning methods (e.g., use coloured diagrams, manipulatives).
Clear, dyslexia-friendly texts: Use larger fonts, avoid clutter, apply colour-coding in worksheets for variables, operators, and numbers.
Chunk tasks: Break down substitution steps — read expression, identify input, substitute, calculate output.
Repeat and reinforce: Use repetition and routine structure to build familiarity.
One-on-one support: Provide prompts and guides for those struggling with abstract concepts.
Use real-life contexts: To anchor abstract algebra in meaningful experiences (e.g., paying for items, calculating total hours and wages).
For advanced learners: Offer extension tasks involving multi-variable functions, exploration of input-output patterns, or creation of functions from scenarios.

Dyslexia-Friendly Reading Options

Use sans-serif fonts (e.g., Arial, Comic Sans) with at least 14-16 pt size.
Print worksheets on pastel-coloured paper (light yellow or blue) to reduce glare.
Use bullet points, avoid dense text blocks.
Highlight keywords such as “substitute,” “input,” “output” in bold or colour.
Provide instructions verbally alongside printed instructions.
Offer reading aloud or paired reading opportunities.

Assessment

Ongoing formative assessment via observation during guided practice and independent work.
Engagement in quiz/game at the end to check conceptual grasp.
Ability to correctly substitute values into functions and interpret outputs.
Use of real-life contexts to demonstrate understanding beyond rote substitution.

Teacher Reflection & Follow-Up

Note which students require more support with substitution or abstract reasoning.
Collect worksheets to review common errors and adapt next lessons accordingly.
Plan subsequent lessons to reinforce these foundational skills or extend into graphing and pattern recognition.

This lesson plan provides a balanced, thoughtful approach suitable for a diverse classroom, ensuring all students gain a solid practical understanding of evaluating functions within the NSW mathematics curriculum framework. It emphasises clarity, repetition, real-world relevance, and inclusive strategies for learners with varying needs.

Teaching Instructions